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Chapter 2: Q37. (page 106)

Solve each equation. Then graph the solution set.

鈭�12b鈭�2=10

Short Answer

Expert verified

The equation 鈭�12b鈭�2=10has solution set as b=鈭�24andb=16and the graph of the solution set is:

Step by step solution

01

Step-1. Define absolute value equation.

For any real numbers a and b, ifa=b and b鈮�0, thena=b or a=鈭�b.

02

Step-2. Formulate case 1 when −12b−2=10.

Simplify the expression for b.

鈭�12b鈭�2+2=10+2鈭�12b脳鈭�2=12脳鈭�2b=鈭�24

03

Step-3. Formulate case 2 when −12b−2=−10.

Simplify the expression for b.

鈭�12b鈭�2+2=鈭�10+2鈭�12b脳鈭�2=鈭�8脳鈭�2b=16

04

Step-4. Plot the graph of the solution set.

From case 1 and case 2, b=鈭�24,16. Plot these values on the number line.

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